Self-consistency constraints on the dynamo mechanism

It is shown that the requirements of self-consistency constrain the functional form of the turbulent dynamo field in an incompressible plasma. These requirements involve the back-reaction of the magnetic field through the Lorentz force in the momentum equation and the conservation laws of magnetohydrodynamic turbulence. The dynamo field is calculated in the weak-field limit when the turbulence is isotropic, as well as in the strong-field limit when the turbulence is anisotropic. For magnetic fields of a nontrivial topology, it is shown that the results of kinematic dynamo theory are strongly modified by the production of hyperresistivity (in the mean-field induction equation) which is left as a remnant after a near-cancellation between the alpha and beta effects. An interpolation formula for alpha quenching, encompassing weak-field and strong-field regimes, is proposed.